If the neutral wire carries current, why do many people believe that it's safe? I've heard "You can touch the neutral wire/bar in the breaker box and not get shocked. Only the hot can hurt you." If the circuit is complete and current is flowing, can't you receive a shock?
The neutral is NOT safe to touch.
When everything is working correctly, it should be at most a few volts from ground. However, and this is the big gotcha, if there is a break in the neutral line between where you are and where it is connected back to ground, it can be driven to the full line voltage. Basically in that case you are connected to the hot line via any appliances that happen to be on in that part of the circuit. Those can easily pass the few mA it takes to kill you.
This is not supposed to happen, but since failures can be lethal and costly, a extra layer of safety is built into the protocol and rules. It is irresponsible and needlessly risky to consider the neutral line safe.
This is why modern appliances either have two prongs and everything is insulated from the user, or three prongs and anything conductive the user can touch is connected to ground. In some past cases there have been appliances with polarized 2-prong plugs, but those are seriously frowned upon today. I don't think you're going to get UL approval for such a device unless it is fully insulated, in which case you shouldn't need a polarized plug.
On a non degraded correctly wired installation the neutral wire is safe because it is at the same potential than the ground terminal.
It is true that it carries current but because there is no voltage difference from ground there is no current passing through when you touch it.
Consider the small appliance with dc transformer power supply such as TV and all appliances that have adaptor or dc transformer. And refer with illustration given by this link . It shows that the primary coil in line 1 is connected to line 2 nothing less and no bargain. The line 1 is a hotline and line 2 is neutral or common line which was actually connected each other. That’s the main reason why the neutral wire is not safe to touch due to the current voltage flowing from one line to another and when can we touch the neutral wire while working? In The Philippines we usually connect the Neutral wire to the ground rod, purposely to make it zero volts wire or the green wire serve as ground should be connected to the appliance. As long as there is a turning coil of wire on your appliance in that particular circuit, the Neutral wire will not be safe to touch unless there is an intimate relationship with the ground.
Under normal conditions the neutral is at close to earth potential but if the neutral goes open circuit then it can rise up to live potential and shock you. Similarly live and neutral could be reversed at some point in the supply system.
So the question then becomes "is the risk of a dangerous voltage on the neutral due to a break in the neutral wiring acceptable?". That is a question that is impossible to answer in the general case as it depends entirely on the circumstances.
On portable appliances I would always unplug before working. I would not consider plugs and sockets and thin flexible cables to be reliable enough to rely on the neutral remaining at earth potential.
On the other hand in the UK it is normal practice to work on circuits of an electrical installation where the neutral is not isolated. I don't know what practices are in other countries.
Going even further many power distribution systems combine the functions of neutral and earth. So do electrified railways.